Appendix F: Miscellaneous
AWG610 Arbitrary Waveform Generator User Manual
Unlike convolution, the result of A×B and B×A are different in correlation. B×A
is calculated as follows (B and A are those from the example on page F–5):
For nonperiodic case:
A×B = b0a4,
b0a3+b1a4,
b0a2+b1a3+b2a4,
b0a1+b1a2+b2a3,
b0a0+b1a1+b2a2,
b1a0+b2a1,
b2a0,
0, (8 points)
For periodic case:
A×B = b0a0+b1a1+b2a2,
b0a4+b1a0+b2a1,
b0a3+b1a4+b2a0,
b0a2+b1a3+b2a4,
b0a1+b1a2+b2a3, (5 points)
Waveforms A and B are regarded as periodic during calculation. The count of the
operation of sum of products is equivalent to the length of the shorter waveform.
The resulting waveform’s cycle equals the same as the longer waveform. The
actual output segment of the waveform corresponds to one cycle. The starting
point value of the waveform equals the sum of the products that is obtained with
the starting point values of waveforms A and B added.